The entropy and enthalpy of lithium intercalation into graphite

Reynier, Yvan; Yazami, Rachid; Fultz, B.

doi:10.1016/s0378-7753(03)00285-4

Cited by 148 publications

(148 citation statements)

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“…The stiffening of the Li vibrational modes in intercalated graphite (with respect to Li metal) reduces the entropy, resulting in a negative intercalation entropy. This effect has 155448-5 been observed experimentally [16,80]. Adding enthalpy and entropy contributions yields an intercalation free energy that is monotonically increasing with temperature.…”

Section: B LI Intercalationmentioning

confidence: 65%

Li intercalation in graphite: A van der Waals density-functional study

2014

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Modeling layered intercalation compounds from first principles poses a problem, as many of their properties are determined by a subtle balance between van der Waals interactions and chemical or Madelung terms, and a good description of van der Waals interactions is often lacking. Using van der Waals density functionals we study the structures, phonons and energetics of the archetype layered intercalation compound Li-graphite. Intercalation of Li in graphite leads to stable systems with calculated intercalation energies of −0.2 to −0.3 eV/Li atom, (referred to bulk graphite and Li metal). The fully loaded stage 1 and stage 2 compounds LiC 6 and Li 1/2 C 6 are stable, corresponding to two-dimensional √ 3× √ 3 lattices of Li atoms intercalated between two graphene planes. Stage N > 2 structures are unstable compared to dilute stage 2 compounds with the same concentration. At elevated temperatures dilute stage 2 compounds easily become disordered, but the structure of Li 3/16 C 6 is relatively stable, corresponding to a √ 7× √ 7 in-plane packing of Li atoms. First-principles calculations, along with a Bethe-Peierls model of finite temperature effects, allow for a microscopic description of the observed voltage profiles.

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Section: B LI Intercalationmentioning

confidence: 65%

Li intercalation in graphite: A van der Waals density-functional study

2014

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“…The label ∆S calc refers to the calculation of the entropy of intercalation (see text). After [232].…”

Section: Lithium Insertion In LI X Coomentioning

confidence: 99%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

571

428

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Abstract. The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered.Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab-initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic x-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information.It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order-disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures.A "quasiharmonic model" is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron-phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phononphonon "anharmonic" interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic ...

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“…The dependency of S on the extent of lithiation of an electrode or state-of-charge of a cell is known as an entropy profile. Half-cells can also be used to compare the entropy profile of a pristine electrode to that of a cycled electrode that has been harvested from a full lithium-ion cell.Entropy [26][27][28][29][30] There have also been numerous reports of the entropy profiles of full lithium-ion cells, 8,26,[31][32][33][34][35][36][37][38][39] which are most useful for incorporation into thermo-electrochemical models. To the best of our knowledge, Yazami and co-workers are the only group to have examined the effect of cycling on the entropy profiles of LIBs.…”

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confidence: 99%

Cycling-Induced Changes in the Entropy Profiles of Lithium Cobalt Oxide Electrodes

Hudak

Davis

Nagasubramanian

2014

J. Electrochem. Soc.

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Entropy profiles of lithium cobalt oxide (LiCoO 2 ) electrodes were measured at various stages in their cycle life to examine performance degradation and cycling-induced changes, or lack thereof, in thermodynamics. LiCoO 2 electrodes were cycled at C/2 rate in half-cells (vs. lithium anodes) up to 20 cycles or C/5 rate in full cells (vs. MCMB anodes) up to 500 cycles. The electrodes were then subjected to entropy measurements (∂E/∂T, where E is open-circuit potential and T is temperature) in half-cells at regular intervals over the approximate range 0.5 ≤ x ≤ 1 in Li x CoO 2 . Despite significant losses in capacity, the cycling did not result in any change to the overall shape of the entropy profile, indicating retention of the LiCoO 2 structure, lithium insertion mechanism, and thermodynamics. This confirms that cycling-induced performance degradation in LiCoO 2 electrodes is primarily caused by kinetic barriers that increase with cycling. Electrodes cycled at C/5 exhibited a subtle, quantitative, and gradual change in the entropy profile in the narrow potential range of the hexagonal-to-monoclinic phase transition. The observed change is indicative of a decrease in the intralayer lithium ordering that occurs at these potentials, and it demonstrates that a cycling-induced structural disorder accompanies the kinetic degradation mechanisms. Lithium-ion batteries (LIB) are the most common power sources for portable electronic devices and emerging electric vehicles. Fundamental understanding of the electrode reactions and degradation mechanisms of such batteries will help lead to improvements in shelf life and operational life (also known as cycle life), which are necessary for the widespread commercialization of LIB-powered electric vehicles.1 To this end, many in situ characterization methods 2 have been developed to characterize LIB electrode reactions during lithiation or delithiation, including X-ray diffraction, 3 synchrotron X-ray techniques, 4 atomic force microscopy, 5 Raman spectroscopy, 6 and transmission electron microscopy.7 Most of these methods require electrochemical cells that are specially designed and electrode materials that are nanostructured or immobilized in a particular fashion. A simple and often overlooked method of battery characterization is the electrochemical measurement of thermodynamic quantities for individual electrode reactions or full electrochemical cells.8 Thermodynamic studies provide fundamental insight into electrode reactions, which can lead to performance improvements, and quantitative information for thermo-electrochemical models of cells and batteries, which are essential for predicting heat generation and preventing thermal runaway. The electrochemical measurement of thermodynamic quantities can be performed as an in situ diagnostic tool for cells or batteries of any form factor, including commercial cells, or as an ex situ evaluation of composite electrodes before or after cycling.The three major thermodynamic quantities for an electrochemical cell are the Gibbs free e...

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The entropy and enthalpy of lithium intercalation into graphite

Cited by 148 publications

References 11 publications

Li intercalation in graphite: A van der Waals density-functional study

Li intercalation in graphite: A van der Waals density-functional study

Vibrational thermodynamics of materials

Cycling-Induced Changes in the Entropy Profiles of Lithium Cobalt Oxide Electrodes

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